Question: Solve for $x$ and $y$ using elimination. ${-6x-y = -21}$ ${5x+y = 19}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-6x-y = -21}\thinspace$ to find $y$ ${-6}{(2)}{ - y = -21}$ $-12-y = -21$ $-12{+12} - y = -21{+12}$ $-y = -9$ $\dfrac{-y}{{-1}} = \dfrac{-9}{{-1}}$ ${y = 9}$ You can also plug ${x = 2}$ into $\thinspace {5x+y = 19}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ + y = 19}$ ${y = 9}$